Your presence status is the setting that tells people your level of availability. The statuses are preset and range from "Available" to "Do Not Disturb".
To change your status click on the button directly below your name (be default this will be labeled "Available") and select your required level of availability.
If you select you status as Do Not Disturb nobody will be able to send you an instant message until you change your status to something else.
Some statuses will be set automatically by Lync:
You can easily see a contact's status by looking at the color that appears next to their name.